Which AI methods are most appropriate for login face recognition?
One of the methods which is quite fast and easy to implement.

You can do Principal Component Analysis (PCA) based face recognition. You can go through this paper for the theory behind it. For an example implementation you can see this blog post. 

The process, roughly, is as following:

If you have a grayscale image of size $(20,20)$, then this image can be flattened to a vector of size $400$. If you have $5$ images of size $(20,20)$ then your data matrix will be of size $(5,400)$. 
We wish to find the principal components of the distribution of faces, or the eigenvectors of the covariance matrix of the data matrix, which will be of size $(5,5)$. Each eigenvector (out of total $5$), of size $(5,1)$, accounts for some amount of variation among the images, and they are ordered by the amount (the eigenvalues corresponding to the eigenvectors) they account for. These eigenvectors can be thought of as a set of features that characterize the variation between the images. Recognition is done by projecting a new image (flattened to size $(400,1)$)into the subspace spanned by the eigenvectors of the covariance matrix and then classifying the face by comparing its coordinates in the face space with the coordinates of the known individuals.

You can see an implementation in this git repo.